# Part D: KAOPEN Interaction — ER Regime & Trade Openness Robustness

Tests whether the Z×KAOPEN compositional shift between trade and income balance is robust to controlling for real-side channels (trade openness, ER flexibility).

## Model Comparison

| Model | Dep Var | N | Countries | R² | ρ |
|-------|---------|---|-----------|----|----|
| M4-base: Z×KAOPEN → Trade Bal | trade_balance_gdp | 4,357 | 150 | 0.279 | 0.872 |
| M5-base: Z×KAOPEN → Income Bal | income_balance_gdp | 4,327 | 150 | 0.162 | 0.803 |
| M4+trade: Z×KAOPEN + Z×trade_open → Trade | trade_balance_gdp | 4,357 | 150 | 0.264 | 0.890 |
| M5+trade: Z×KAOPEN + Z×trade_open → Income | income_balance_gdp | 4,327 | 150 | 0.129 | 0.817 |
| M4+ERS: Z×KAOPEN + Z×ERS → Trade | trade_balance_gdp | 3,959 | 138 | 0.349 | 0.864 |
| M5+ERS: Z×KAOPEN + Z×ERS → Income | income_balance_gdp | 3,933 | 138 | 0.210 | 0.787 |

## Key Interaction Coefficients

| Variable | Model | Coef | SE | p-value |
|----------|-------|------|----|---------|
| Z_1_x_kaopen | M4-base: Z×KAOPEN → Trade Bal | 57.3659*** | 8.6374 | 0.0000 |
| Z_1_x_kaopen | M5-base: Z×KAOPEN → Income Bal | -37.1958*** | 6.9785 | 0.0000 |
| Z_1_x_kaopen | M4+trade: Z×KAOPEN + Z×trade_open → Trade | 13.0365 | 8.8728 | 0.1418 |
| Z_1_x_kaopen | M5+trade: Z×KAOPEN + Z×trade_open → Income | -27.2183*** | 7.4299 | 0.0003 |
| Z_1_x_kaopen | M4+ERS: Z×KAOPEN + Z×ERS → Trade | 63.2076*** | 8.7756 | 0.0000 |
| Z_1_x_kaopen | M5+ERS: Z×KAOPEN + Z×ERS → Income | -38.3132*** | 7.0373 | 0.0000 |
| Z_2_x_kaopen | M4-base: Z×KAOPEN → Trade Bal | -8.8990*** | 1.3330 | 0.0000 |
| Z_2_x_kaopen | M5-base: Z×KAOPEN → Income Bal | 5.5578*** | 1.0770 | 0.0000 |
| Z_2_x_kaopen | M4+trade: Z×KAOPEN + Z×trade_open → Trade | -2.4139* | 1.3634 | 0.0767 |
| Z_2_x_kaopen | M5+trade: Z×KAOPEN + Z×trade_open → Income | 4.2303*** | 1.1396 | 0.0002 |
| Z_2_x_kaopen | M4+ERS: Z×KAOPEN + Z×ERS → Trade | -9.7454*** | 1.3585 | 0.0000 |
| Z_2_x_kaopen | M5+ERS: Z×KAOPEN + Z×ERS → Income | 5.7121*** | 1.0889 | 0.0000 |
| Z_3_x_kaopen | M4-base: Z×KAOPEN → Trade Bal | 0.3693*** | 0.0554 | 0.0000 |
| Z_3_x_kaopen | M5-base: Z×KAOPEN → Income Bal | -0.2251*** | 0.0448 | 0.0000 |
| Z_3_x_kaopen | M4+trade: Z×KAOPEN + Z×trade_open → Trade | 0.1126** | 0.0565 | 0.0462 |
| Z_3_x_kaopen | M5+trade: Z×KAOPEN + Z×trade_open → Income | -0.1765*** | 0.0471 | 0.0002 |
| Z_3_x_kaopen | M4+ERS: Z×KAOPEN + Z×ERS → Trade | 0.4016*** | 0.0566 | 0.0000 |
| Z_3_x_kaopen | M5+ERS: Z×KAOPEN + Z×ERS → Income | -0.2302*** | 0.0453 | 0.0000 |
| Z_1_x_trade_open | M4+trade: Z×KAOPEN + Z×trade_open → Trade | 3.4936*** | 0.3130 | 0.0000 |
| Z_1_x_trade_open | M5+trade: Z×KAOPEN + Z×trade_open → Income | 0.0795 | 0.2643 | 0.7635 |
| Z_2_x_trade_open | M4+trade: Z×KAOPEN + Z×trade_open → Trade | -0.4939*** | 0.0479 | 0.0000 |
| Z_2_x_trade_open | M5+trade: Z×KAOPEN + Z×trade_open → Income | -0.0372 | 0.0404 | 0.3565 |
| Z_3_x_trade_open | M4+trade: Z×KAOPEN + Z×trade_open → Trade | 0.0193*** | 0.0020 | 0.0000 |
| Z_3_x_trade_open | M5+trade: Z×KAOPEN + Z×trade_open → Income | 0.0022 | 0.0017 | 0.1925 |
| Z_1_x_ers | M4+ERS: Z×KAOPEN + Z×ERS → Trade | -11.0846 | 26.1574 | 0.6718 |
| Z_1_x_ers | M5+ERS: Z×KAOPEN + Z×ERS → Income | 4.2382 | 23.8639 | 0.8590 |
| Z_2_x_ers | M4+ERS: Z×KAOPEN + Z×ERS → Trade | 1.5800 | 4.0412 | 0.6958 |
| Z_2_x_ers | M5+ERS: Z×KAOPEN + Z×ERS → Income | -0.2931 | 3.6879 | 0.9367 |
| Z_3_x_ers | M4+ERS: Z×KAOPEN + Z×ERS → Trade | -0.0643 | 0.1674 | 0.7011 |
| Z_3_x_ers | M5+ERS: Z×KAOPEN + Z×ERS → Income | 0.0043 | 0.1528 | 0.9776 |
| trade_openness | M4+trade: Z×KAOPEN + Z×trade_open → Trade | -0.0122 | 0.0109 | 0.2644 |
| trade_openness | M5+trade: Z×KAOPEN + Z×trade_open → Income | 0.0065 | 0.0085 | 0.4457 |
| ers_index | M4+ERS: Z×KAOPEN + Z×ERS → Trade | 0.2308 | 0.8523 | 0.7866 |
| ers_index | M5+ERS: Z×KAOPEN + Z×ERS → Income | -0.6653 | 0.7773 | 0.3921 |